The management of investment portfolios has been the subject of substantial theory and research. Portfolio theory considers how wealth should be invested and how to maximize a portfolio's expected return for a given amount of portfolio liquidity-adjusted risk, or, equivalently, minimize liquidity-adjusted risk for a given level of expected return, by carefully choosing the proportions of various assets. While a certain rate of return may be expected, the valuation of individual holdings in the portfolio can depart upward or downward from that expected rate of return. This upward and downward variation from the expected value is known as variance, or volatility. Over time, securities, in theory, should have an efficient frontier for expected volatility and return. According to theory, securities with a higher expected risk will have a higher expected return.
Financial indices are often used to benchmark the performance of a financial instrument. The S&P 500® Index is an example of one such benchmark for stock-oriented funds and the Barclays Aggregate Bond Index is an example of a benchmark for bond funds. The S&P 500® is the largest equity benchmark in the world. Trillions of dollars are either invested in this benchmark or in funds benchmarked to it. Since yearend 1999, U.S. broad market indices such as the S&P 500® have experienced long periods of underperformance. For example, an investor in the S&P 500® at yearend 1999 was down approximately 20% 10 years later in nominal terms at yearend 2009, depending on fees and treatment of dividends. It was not until late 2012 that the S&P 500® had a positive nominal return for these yearend 1999 investors, including many large pension funds and endowments. As of October 2014, the S&P 500® had a negative real return since yearend 1999. During this same period, broad-based funds holding U.S. government or corporate debt have had positive real returns with corporate debt earning more than government debt during this period. This premium was due to the extra risk of a corporate bond versus a U.S. government bond of comparable duration. These markets had their annual fluctuations, but have been fairly stable over a reasonable period of time, these securities had both positive returns and differences that would be expected based on risk. Neither of these statements can be made for equity indices such as the S&P 500® that lost value on an absolute basis and underperformed materially over a long period of time with respect to the less risky indices holding investment-grade corporate or government debt.
Given a cap-weighted methodology, a change in the market value of a relatively large company has a disproportionate effect on an equity index, while a change in the debt outstanding of a relatively highly indebted issuer has a disproportionate effect on a fixed income index. Funds that track these indices also experience the corresponding fluctuations in value as the instruments representing the relatively larger companies fluctuate in value.
The S&P 500®, like most broad market indices, is capitalization-weighted. This means that the weight of an individual company in the index is proportional to its market capitalization relative to the other constituents. There are no controls in the S&P 500® to ensure that a single security or groups of securities that share a common risk do not become overweighted to represent too large a proportion of the portfolio. That is, the types of controls used in scientific fields and engineered processes where population controls are used to limit the influence that one part of a population can have on a total population being measured are not used in the broad market indices. Such controls limit both positive and negative influences. In population studies, controls are used to produce a normative model of an underlying population. Because there are no controls in the benchmarks currently used to invest in equity securities, there is no assurance that historical returns from yearend 1999 to the present are representative of equity securities in general. The strategy of capitalization-weighting without controls has produced below-average returns for long periods of time.
The results of the major U.S. broad-market equity indices since 1999 appear to be inconsistent with the main theories of the pricing of investment securities and the theory of efficient markets. Much of the work on efficient markets and asset pricing followed the pioneering work of Markowitz and Sharpe with later notable additions by others such as Fama and French. Their theories suggest that individual securities are priced at a level that is expected to produce a risk-adjusted return relative to other investment securities and that, by following certain rules, a portfolio of securities has a higher probability than an individual security of achieving this risk-adjusted rate of return in any given period or over several periods.
The principles that Markowitz and others proposed have been used to assist investors and managers in the selection of the most efficient portfolio design by analyzing various possible portfolios of a given set of securities. By delineating a portfolio construction process that entails choosing securities whose risk-return profiles diverge significantly, the models show investors how to reduce their risk. The foundational model in this area is known as the mean-variance model because it is based on expected returns (mean) and the distribution from expected returns (variance) of the various portfolios. When developing the original mean-variance model, Markowitz made the assumption that a portfolio that maximizes return for a given risk or minimizes risk for a given return is an efficient portfolio. Thus, portfolios are selected using the following rules: (a) from the portfolios that have the same expected return, the investor will prefer the portfolio with lower risk, and (b) from the portfolios that have the same risk level, an investor will prefer the portfolio with higher expected rate of return.
To facilitate portfolio construction, Markowitz used the expected covariance or correlation among securities as an additional input that would enable investors to maximize their risk-adjusted return at the portfolio level. Although an individual security may underperform for a long period of time, the rules developed for efficient portfolio construction were designed to reduce, through diversification, this probability of underperformance with respect to the portfolio of securities. According to these foundational theories, investors could expect to be compensated only for systematic, or broad-market, risks, with a premium commensurate with the risks of a given asset class, and should be able to diversify away their exposure to non-systematic risks at the efficient frontier, consisting of the hypothesized market portfolio.
One explanation for the inconsistency between modern portfolios and the theoretical portfolios on which the efficient market hypothesis was developed is that modern portfolios operate at a much greater scale and level of complexity than the theoretical examples. The early theoretical models based on the efficient market hypothesis and capital asset pricing model tend to use individual securities and describe diversification within portfolios consisting of numbers of securities that are in the single digits and low double digits. Many of the foundational papers were written before the mutual fund boom of the 1980s and 1990s following the creation of individual retirement accounts (IRAs) by the Employee Retirement Income Security Act (ERISA) of 1974, as well as the introduction of the first index fund in 1976. For example, the Markowitz paper on portfolio selection published in the Journal of Finance was written in 1952. According to the first shareowner census undertaken by the New York Stock Exchange (NYSE) in 1952, only 6.5 million Americans owned common stock at the time (about 4.2% of the U.S. population), and each held an average of four stocks. Sharpe's paper, “A Simplified Model for Portfolio Analysis,” was written in 1963 and his book, “Portfolio Theory and Capital Markets,” was written in 1970, long before the mutual fund boom created by ERISA, the advent of globalization and modern technology, the development of exchange-traded products enabling retail investors en masse to hold thousands of securities at once, or the widespread recognition by institutional investors of the unique problems associated with managing such large funds.
Modern portfolios manage trillions of dollars in the aggregate. The total investment into US mutual funds was $13 trillion dollars in 2012. In order to reduce exposure to non-systematic risks while avoiding relatively illiquid positions, the portfolios require thousands of securities in diverse risk groups. At this scale, lacking applicable financial theory to guide selections and weights, as portfolio theory was developed for portfolios of a much smaller scale, building efficient portfolios has been challenging. The absolute scale of investment today by very large institutions has grown exponentially since the mutual fund boom of 80s and 90s, discussed above. In addition, the underlying population of securities has grown in heterogeneity and complexity. This diversity and interconnectedness is increasing every year. The need to control for the non-systematic risks embedded in this portfolio of companies also increases every year.
There is a need for a framework that enables the systematic comparison and contextualization of all types of securities in today's complex heterogeneous global market. Specifically, there is a great need for a framework that enables systematic comparison and contextualization of all types of equities in today's complex heterogeneous global market. A systems approach to organizing economic and financial information would accomplish this by enabling us to interrelate the vast data related to these activities and analyze economic and financial interdependencies.
In addition, there is a need for a new normative methodology for constructing portfolios of investment securities, one that addresses the complexities of today's companies and the increasing size and diversity of today's funds by applying the approach and foundational principles of Markowitz and Sharpe to the complexities of today's large-scale funds.
Some efforts for portfolio construction attempt to address the complex heterogeneous global market by relying on existing systems for classifying companies. Current systems of classification, such as Global Industry Classification Standard (GICS), are not well-suited for building new models of potential efficient portfolios of these large-scale modern investment vehicles that draw upon complex and globally interrelated universes of equities. The NAICS or GICS relate companies by their positions in a fixed hierarchy. There are two significant limitations of the fixed NAICS and GICS hierarchies: 1) any items without a common parent are unrelated and cannot be compared using terms in the hierarchy; 2) any items sharing a parent can only be compared along the terms that GICS or NAICS uses to label that group (insofar as the names of the groups indicate the term that separates them, e.g., “consumer” versus “commercial” may relate to the customer base).
These systems, similar to the foundational papers in finance, were created before the advent of large digital databases; they are modeled after the frameworks of the time such as the Dewey Decimal System and Standard Industry Classification System. Those systems rely on a fixed hierarchy in which each entity has a single parent; that parent has a single parent, and so on. Each parent has descriptions, but not concepts of specific attributes that would enable an entity under one parent to be related to an entity under another parent.
Without the ability in the data structure to relate an entity under one parent to an entity under another parent, it is hard to understand the multivariate risks to which companies are exposed and, thus, to see how many securities in a large portfolio or index may share a similar or related risk. The shortcomings of current classification systems are becoming increasingly apparent given the complexities of today's companies and the increasing size and diversity of today's funds. Although many of the biggest risks in a capitalization-weighted strategy result from the lack of controls for single risk exposures, bubbles, or massive non-systematic price corrections, there are currently limited tools to systematically address these problems. Thus, there is a need for a multivariate attribute-driven categorization system enabled by current data processing capable of providing these tools as well as the ability to build multiple different portfolios to assess the efficiency of each and test for a normative case.
Benchmarks
In addition to the systems used to organize securities and the information about them, modern portfolio construction is challenged by another step of the process which has been slow to evolve: the benchmarks against which to compare their performance. In other areas of economics and finance, the role of benchmarks has been well established. Central banks routinely use inflation targets to guide policy, which has proved instrumental in increasing the predictability of price changes. This has enabled consumers, merchants, and investors to consume, save, and invest with a high degree of confidence in near to medium-term price changes. National economic ministries routinely project their future annualized GDP growth and seek to achieve it, which multilateral institutions, banks, and investors rely on as an index of a country's economic health.
In corporate finance, publicly traded companies regularly issue earnings guidance and have quarterly earnings targets, which it is the CFO's principal role to achieve. Companies are benchmarked against their earnings targets and held accountable for them by boards and financial analysts, and even minor shortfalls in earnings frequently lead to precipitous drops in stock price. CFOs are also expected to deliver on target returns on equity, which, since it is junior to debt in the capital structure, has a higher cost of capital for a given company and should have higher returns than the debt issued by a company. In each case, modern technology has enabled decision makers to more accurately forecast future economic and financial outcomes, control for risk, and achieve their benchmarks with a high degree of predictability.
At the portfolio level, however, there is no comparable accountability for equity benchmarks. Since equity investments are riskier than debt investments at the portfolio level all equity indices should strive to earn a consistent premium to corporate long-term bonds. Just as all companies will expect a higher cost of equity than debt financing, all equity investors' indices, like the companies they invest in, should anticipate a higher return when they invest in a company's equity rather than its debt issuances. Because of the statistical properties of large sets of securities, investors should expect to see this risk premium even more consistently in an index portfolio. This risk premium should be realized at the portfolio level; equity index investors should strive to beat corporate long-term bond returns for their constituent group on a consistent basis.
The capital asset pricing model uses the term alpha to describe outperformance of a benchmark; from a company's perspective, generating alpha entails beating its return projections. For any given company, an equity premium is commensurate with achieving earnings estimates and outperforming borrowing rates. The same principle should hold at the portfolio and index level; investors in portfolios of equities should expect returns that are higher than the average borrowing rate for the bonds of a given constituent group. If an index or portfolio does not achieve the performance target predicted by theory, a new methodology is required that will realize that target more consistently and predictably.
The S&P 500 is widely accepted as an equity benchmark even while it continues to lack risk controls and exhibit higher volatility than predicted by theoretical models. It fails to achieve the rates of return predicted for it by the foundational finance theories and asset pricing models. Nevertheless, the methodology of the S&P 500 has not changed significantly since its inception, and it has failed to capitalize on the tools of modern technology and data analytics to control for risk and achieve more predictable, reliable rates of return. Thus, there is a need for a reconsideration of how to construct equity benchmarks and the standards for them.
Conglomerates
Corporations have sought to achieve diversification at the company level through the conglomerate form, which involves acquiring and managing multiple independently operated and often functionally unrelated businesses through a parent company. Owners of conglomerates sought to reduce the volatility in earnings associated with business cycles in various industries by organizing relatively uncorrelated income streams under the same corporate structure; some also sought to achieve cost savings through synergies in procurement, branding, marketing, and sales, to avoid antitrust restrictions on expansion and consolidation in a particular industry by aggregating interests across multiple sectors.
Although conglomerates have enjoyed substantial popularity in certain wealthy countries following long periods of high economic growth—the U.S. in the 1960s, Japan in the 1980s, and more recently, South Korea—they have largely fallen out of favor in high-income markets. The extra layers of bureaucracy and lack of sufficient industry expertise at the holding or parent company level frequently have made conglomerates too complex to manage effectively.
More recently, private equity firms have sought to achieve similar objectives to those of conglomerate managers by acquiring and managing mature businesses, frequently in a wide variety of industries. The significant fees charged by such firms, typically comprising 2% of assets managed and 20% of returns over a benchmark in addition to deal-specific fees, have impeded their ability, as a group, to generate high returns to investors, while other firms have foundered due to similar challenges that confronted conglomerates, failed to capitalize on potential marketing, sales, and operational synergies, or incurred excessive leverage that contributed to large losses during economic downturns.
While some private equity firms consistently have shown very strong performance, most of them are limited partnerships inaccessible to the general public due to regulatory restrictions, and the information regarding their operations, strategy, and investments is largely opaque and frequently unavailable. The lack of transparency and liquidity in these funds, as well as the challenges involved in managing businesses across disparate sectors, have impeded the capacity of these firms to scale. At present, the largest traditional investment firm itself manages more capital than the entire global private equity industry combined.
Volatility
Volatility in pricing refers to fluctuations in price. Volatility is a significant factor in portfolio performance and these price fluctuations may create a drag on portfolio growth. For example, daily volatility has been shown to hurt the return of leveraged exchange-traded funds. Random movements in investment securities without controls at the portfolio level, especially large downward movements caused by unpredictable events or the popping of non-systematic bubbles, reduce risk and liquidity-adjusted returns. In these cases, there is little to no expectation that portfolios and their constituent investment securities will rebound to pre-existing levels. In both of these cases, the securities being impacted are being re-priced because of new information or a sudden market recognition that they were overpriced.
In an effort to reduce the effects of volatility on a portfolio, various weighting schemes have been proposed in the investment industry. For example, one method described in U.S. Pat. No. 8,306,892 operates by calculating weights based on market capitalization, gross-domestic product, and geographic region. In another example, described in U.S. Pat. No. 8,131,620, weights in a portfolio of securities are based on market capitalization and dividend yield. Numerous other portfolio weighting schemes exist. However, none of these weighting schemes fully address the shortcomings of prior art portfolio theory, as discussed above. Some examples, such as that described in U.S. Pat. No. 8,005,740, use accounting-based metrics for weighting securities universes.
In prior art portfolio construction, random groups of securities are likely to have periods of significant valuation swings, both up and down, from one time period to another. These massive swings in value in random groups of securities may not be caused by variables such as accounting attributes or their designation as “growth” or “value” stocks. The valuation swings could be caused by, for instance, companies being long a specific commodity when the commodity suddenly loses its value; over-exuberance in the demand prospects for a company's or industry's product that does not meet demand; long fixed-cost contracts when the actual costs available to their competitors changes; over-weighting of a certain asset in the product mix when that asset loses its value; or other idiosyncratic reasons.
There are many reasons for apparently random bubbles. In some cases, they are systematic or broad-market bubbles; in others, they are largely limited to a constituent group (such as an asset class or industry). There are certain events that appeared to be systematic because they impacted index and portfolio returns so severely, such as the Internet bubble of the late 1990s, but are non-systematic. In either case, the impact on an investor's returns when the bubbles collapse can be extremely negative as a result of portfolio biases and overexposure to constituents that are especially impacted by the collapse of the bubble.
The random walk hypothesis in financial theory represents the inability to address the apparent randomness of volatility and returns in equity-based investment securities. The hypothesis implies that in an efficient market, a large random selection of equity-based investment securities will perform as well as an actively-managed selection of equity-based securities, before adjusting for taxes and fees. The random walk hypothesis is the underlying reason for the proliferation of index funds and the broad support for passive index funds by the academic community. The hypothesis, taken to its logical extreme, suggests that a blindfolded monkey throwing darts at the stock listings could select a portfolio that would do just as well as one selected by the experts.
Many different weighting strategies have been proposed to deal with this problem of random volatility in equity-based investment securities. The recent underperformance of these passive capitalization and even-weighted indices to debt indices that track comparable universes of companies has highlighted that these passive indices continually affirm the same randomness hypothesis.
A major problem in the risk management of large portfolios of securities is the inability in existing systems to control for the occurrence of these types of events without a framework to define homogeneous subpopulations. If a portfolio inadvertently over-weights in a security or groups of securities that have a common bubble or bankruptcy risk, the returns can be materially impacted by a relatively small number of securities in the portfolio. Non-systematic bubbles and bankruptcies are associated with non-systematic factors of the industries, companies, or assets associated with specific investment securities. In several cases, over-weighting in specific non-systematic variables has caused significant negative impacts on a portfolio. This was clearly the case of the Internet bubble. In calendar year 2000, the capitalization-weighted S&P 500® was down 9.09%. In that year, there were 16 stocks that were down 49.8%, while the rest of the market was up 4.28%. Unfortunately for investors in funds tracking that index, these 16 companies, which were all in the business of moving, storing, or processing information, comprised 24.8% of the total portfolio. The underperformance of these select securities had a massively disproportionate effect on the index, and the trillions of dollars in funds benchmarked to it, because of the lack of controls on the underlying index.
Prior efforts to improve portfolio returns generally appear to have at least three problems: 1) a sub-optimal number of groups; 2) insufficient ability to control for covariance within groups or correlation among groups to ensure that each group operates in a predictable group-specific way; and 3) no way of defining a group in a systematic way that is applicable across an entire economy and permits all groups to be related to one another. Existing large-scale heterogeneous indices and portfolios of securities lack controls on their constituent groups and neither capitalization-weighting nor even weighting are capable of reducing the impact of group-specific risks at the portfolio level in a population of securities.
Covariance and Correlation
While finance theorists have made significant breakthroughs in forecasting the return and variance for individual securities, there has been little advancement in finding reliable indicators of the pairwise correlations or covariances between securities, a required input to the Markowitz model. In 1973, financial economists Edwin Elton and Martin Gruber addressed why quantitative solutions are unlikely to be practicable at scale, and noted that to obtain efficient portfolios from among 200 stocks, 19,990 correlation coefficients would have to be produced.
There are also institutional impediments to finding generally applicable and sufficiently explanatory indicators, as there is highly unlikely to exist any individual at a financial institution sufficiently familiar with the mathematical analysis of each constituent of a substantial equity universe to be able to approximate a quantitative solution. Elton and Gruber concluded that there is no non-overlapping organizational structure that would permit security analysts in a financial institution to produce estimates of correlation coefficients between all relevant pairs of stocks, since each analyst follows a subset of the stocks in which the institution has an interest.
In an effort to address the lack of reliable indicators of the correlation in how securities perform, traditional models such as the capital asset pricing model (CAPM) assume that all residual pairwise correlations are zero. That is, it is assumed that each security has no relationship to any other security in excess of co-movement with the market as a whole. This assumption lacks realism: a simple likelihood ratio test for zero correlations rejects the null hypothesis of zero residual pairwise correlations at the 0.000001 significance level.
Elton and Gruber illustrate that the CAPM can be improved upon simply by assuming a single nonzero pairwise correlation to be assigned across an entire portfolio, but acknowledge the severe limitations of this approach. The challenges referenced above, and the lack of a well-developed, field-specific framework to address the covariance issue at scale, have left the problem unsolved. The increasing scale, complexity, and heterogeneity of modern portfolios have made this challenge more acute.
Purely quantitative measures of correlation have proven least accurate and least predictive precisely when they are most needed: during bubbles, crashes, and other periods of high market volatility, when these measures have deviated far from their historical norms. Investors who have sought to diversify principally based on quantitative historical covariances have sustained extraordinary losses during recent periods of market volatility.
Factor Models
Asset pricing models such as the CAPM frequently have failed to accurately describe or predict performance characteristics of securities, groups of securities, or portfolios. These models isolate a very small number of factors believed to be driving security price returns and are predicated on the assumption that they can be determined purely quantitatively.
The CAPM relies on the risk free rate, the market return, and the idiosyncratic risk of the security; in other words, it is predicated on the assumptions (among others) that there is one factor F common to all securities in the market, there exist a set of factors f1,2 . . . n which map precisely, in a one-to-one correspondence, to the set of securities s1,2 . . . n, that these factors and their weights are essentially stable over time, and that the relationship among these factors and their weights is entirely unknown.
The Fama-French three-factor model adds size and book to market value to the aforementioned factors, while their posited five-factor model, which, as of November 2013, also adds profitability and asset growth, does not yet appear to improve on their previous model. (Eugene Fama and Kenneth French, “A Five-Factor Asset Pricing Model,” working paper, September 2014.) Carhart's posited four-factor model adds momentum to the three-factor model. (Carhart, M. M., “On Persistence in Mutual Fund Performance,” The Journal of Finance 52: 57-82 (1997).) Tobias Adrian, Emanuel Moench, and Hyun Song-Shin point to the systemic impact of aggregate broker-dealer capital structure and asset growth in non-banking financial institutions on equity and bond prices. (Tobias Adrian, Emanuel Moench, and Hyun Song Shin, “Financial Intermediation, Asset Prices, and Macroeconomic Dynamics,” Federal Reserve Bank of New York, 2010.) Andrew Lo and Amir Khandani add common factors such as general market volatility and commodity prices, and emphasize liquidity as an additional factor at the security level which was unduly neglected in studies of large and mid-cap stocks in developed markets during periods of little turbulence, when liquidity factors are less relevant. (Andrew Lo and Amir Khandani, “Illiquidity Premia in Asset Returns,” draft paper, June 2009.)
Methodologies focusing first on quantitative analysis that have failed to identify any factors or risks other than systematic and idiosyncratic, or the relationship among the various idiosyncratic factors or risks, and a lack of computing power when many of the key paradigms of finance were formulated, have led portfolio and index construction to be predicated on the assumption that all drivers of security price returns either a) affect every security in the entire market precisely the same way, or b) affect only one security in the entire market in any way at all. This untenable assumption has made effective portfolio and index construction extremely difficult.
Problems of Scale
For multiple reasons, the problems described above are particularly acute in large-scale portfolios of securities. Various reasons why management at scale is difficult are provided below.
(a) Charter limits on ownership: For many funds and fund managers, there are limits on the percentage of a company they can own. For example, for any fund that seeks to acquire a 5% holdings of U.S. public equities, there are required 13-D filings and more extensive regulatory oversight. Many funds will not or cannot cross that threshold.
(b) Liquidity limits on ownership: The more a fund owns of an individual security, particularly for large holdings, the harder it generally is to sell. The effect is frequently trivial for small dollar value holdings in liquid securities, but may be significant for larger holdings or relatively illiquid securities.
(c) Large funds need a large number of securities to fill out a portfolio: Due to the factors identified above as well as other practical issues, a large fund needs a large number of companies to invest in due to liquidity and ownership issues. Across an economy, there are many linkages among companies, and the larger the number of companies under evaluation, the more difficult it is to track and oversee the linkages and risks that come from them.
(d) Large funds may face a limited selection of securities: Due to the factors identified above as well as many more practical issues, large funds often need to invest disproportionately in large companies or other funds. The available companies in this group vary over time. In addition, these securities have variable weights and aggregate differently depending on what companies exist in which category at any given point in time.
(e) Geographic variation: In addition to changes over time, this industry, sector, or company selection varies by geography; in large portfolios, indices, or funds comprised of securities, determining the geographic exposure of assets, operations, and products, as non-limiting examples, is impracticable using prior art methods. Sector differentiation may be a greater cause of price movements between geographies than the underlying currency that drives the products. For example, portfolios of US securities are often more heavily weighted in technology stocks than portfolios of European or Latin American securities. Europe and Latin America are relatively heavy in manufacturing and financials.
If a fund, index, or portfolio manager's goal is currency differentiation, it is important to control for these sector variations. Not only understanding the different potential risk groups that exist at any given point in time and in any specific geography or category, but also being able to control for these risks is difficult using currently or previously known techniques.
(e) Attribute and overconcentration risk are multi-dimensional: Single and multiple attributes are helpful in distinguishing risks in individual companies, but attributes that are clear on an individual level are lost in larger classification systems. These varied, yet critical, attributes impacting security price returns are often aggregated into one technology metacategory in large-scale funds. The existing categories in current systems tend to be standardized on a global basis and do not permit differentiation among these attributes that aggregate to characterize each metacategory. The inability to represent linked multi-attribute risks is a significant limitation for existing large-scale investment portfolios.
If portfolios, and large-scale portfolios in particular, are not better controlled, and the linkages between companies are not well understood, non-systematic events can appear to have systematic impact. Examples of non-systematic events are provided below. Known and existing classification systems do not address the underlying statistical causes for the systematic impact of the volatility of the constituents of large-scale portfolios of securities. With improved controls, however, the impact of non-systematic events could be limited.